In the EFT calculation
the choice of the time dependence of the propagators in these 5PN cases turns out to be irrelevant in
the explicit calculation, since the causal and the in–in formalism lead to the same result.
The reason for this is that the internal multipole moment, either \(E\)  or \(L^k\) , is a conserved quantity, implying a
\(\delta \) –distribution for the energy components at their vertex. The
associated propagator is therefore an (effective) space–like potential and the corresponding diagram only
depends on a single
energy variable, \(k_0\) . In the case of the potential terms, cf. [1]}, [2]},
the reason for the same agreement is different. Here the propagators in Fourier–space are expanded as
\(\frac{1}{\vec{k}^2 - k_0^2 \pm i \varepsilon } = \frac{1}{\vec{k}^2} \sum _{l=0}^\infty \left(\frac{k_0^2}{\vec{k}^2}\right)^l,\) 
